Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
562 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20287690 | C2 | semidirect |
| 2. Q8×D424 | C2 | semidirect |
| 3. #20276939 | C2 | semidirect |
| 4. #20276853 | C2 | semidirect |
| 5. #20276751 | C2 | semidirect |
| 6. C4×D848 | C2 | semidirect |
| 7. Q8×C16×C53 | C2 | semidirect |
| 69. D424 | #41 | semidirect |
| 74. Q8×C53 | D16 | semidirect |
| 111. Q8×C16 | D53 | semidirect |
| 134. C53 | #33925 | semidirect |
| 186. Q8 | D848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287690 | 2 |
| Q8×D424 | 2 |
| #20276939 | 2 |
| #20276853 | 2 |
| #20276751 | 2 |
| C4×D848 | 2 |
| Q8×C16×C53 | 2 |
| #33925 | 53 |